{
  "abstract": "We study a class of mean-field control (MFC) problems with singular controls over a finite horizon, allowing for general dependence of the cost functional on the measure argument. We derive an auxiliary mean-field game (MFG) with singular controls, which we refer to as a potential MFG, and show that, under suitable convexity assumptions, any solution to this potential MFG yields a solution to the original MFC problem. We apply this general result to a version of the classical Monotone Follower Problem by I. Karatzas and S. E. Shreve (SIAM Journal on Control and Optimization 22(6), pp. 856-877, 1984) with scalar mean-field interaction. The associated potential MFG with singular controls is solved by exploiting its connection with optimal stopping for the optimization step and by a suitable application of the Kakutani-Fan-Glicksberg fixed-point theorem. In the case of strategic complementarities, the mean-field equilibrium (and hence the optimal policy of the original MFC problem) is characterized by a continuous nonincreasing free boundary that uniquely solves a nonlinear integral equation. To the best of our knowledge, this is the first paper to provide a complete characterization of the optimal policy in a finite-horizon mean-field singular stochastic control problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.26808",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrea Amato"
    },
    {
      "name": "Federico Cannerozzi"
    },
    {
      "name": "Giorgio Ferrari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3m3nnvktz6m1s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.26808",
  "fulltext_url": null,
  "id": "3m3nnvktz6m1s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.26808",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7171869575",
  "pdf_url": "https://arxiv.org/pdf/2607.26808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3m3nnvktz6m1s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.26808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.26808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On Mean-field Singular Stochastic Control Problems",
  "title_text": "On Mean-field Singular Stochastic Control Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3m3nnvktz6m1s",
  "venue": "arXiv",
  "versions": []
}